On A 5-Dimensional Spinning Cosmic String

We present a numerical solution of a stationary 5-dimensional spinning cosmic string in the Einstein-Yang-Mills (EYM) model, where the extra bulk coordinate $\psi$ is periodic. It turns out that when $g_{\psi\psi}$ approaches zero, i.e., a closed time-like curve (CTC) would appear, the solution becomes singular. When a negative cosmological constant is incorporated in the model, the solution becomes regular everywhere with angle deficit$<2\pi$. However, the cosmic string-like object has not all the desired asymptotic properties of the counterpart Abelian Nielsen-Olesen string. When we use a two point boundary value routine with the correct cosmic string features far from the core, then again a negative $\Lambda$ results in an acceptable string-like solution. We also investigated the possibility of a Gott space time structure of the static 5D cosmic string. The matching condition yields no obstruction for an effective angle deficit. Moreover, by considering the angular momentum in bulk space, no helical structure of time is necessary. Two opposite moving 5D strings could, in contrast with the 4D case, fulfil the Gott condition.